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<a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,5,-3,1).
G.f.: (x^7-3*x^6+3*x^5-2*x^4+x^3-3*x^2+3*x-1)/((x^3-x^2+2*x-1)*(x-1)^2). - Alois P. Heinz, Feb 10 2019
nonn,more,easy,changed
More terms from Alois P. Heinz, Feb 10 2019
1, 1, 1, 2, 6, 12, 23, 44, 82, 149, 267, 475, 841, 1484, 2613, 4595, 8074, 14180, 24896, 43702, 76705, 134622, 236260, 414623, 727629, 1276917, 2240851, 3932438, 6900967, 12110373, 21252244, 37295110, 65448378, 114853920, 201554603, 353703696, 620706742
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1, 1, 1, 2, 6, 12, 23, 44, 82, 149, 267, 475, 841, 1484, 2613, 4595, 8074, 14180, 24896, 43702, 76705, 134622, 236260, 414623, 727629, 1276917
allocated for Gus WisemanNumber of ways to split an n-cycle into connected subgraphs, none having exactly two vertices.
1, 1, 1, 2, 6, 12, 23, 44, 82, 149, 267, 475, 841, 1484, 2613, 4595, 8074, 14180, 24896, 43702, 76705
0,4
The a(1) = 1 through a(5) = 12 partitions:
{{1}} {{1}{2}} {{123}} {{1234}} {{12345}}
{{1}{2}{3}} {{1}{234}} {{1}{2345}}
{{123}{4}} {{1234}{5}}
{{124}{3}} {{1235}{4}}
{{134}{2}} {{1245}{3}}
{{1}{2}{3}{4}} {{1345}{2}}
{{1}{2}{345}}
{{1}{234}{5}}
{{123}{4}{5}}
{{125}{3}{4}}
{{145}{2}{3}}
{{1}{2}{3}{4}{5}}
cyceds[n_, k_]:=Union[Sort/@Join@@Table[1+Mod[Range[i, j]-1, n], {i, n}, {j, Prepend[Range[i+k, n+i-1], i]}]];
spsu[_, {}]:={{}}; spsu[foo_, set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@spsu[Select[foo, Complement[#, Complement[set, s]]=={}&], Complement[set, s]]]/@Cases[foo, {i, ___}];
Table[Length[spsu[cyceds[n, 2], Range[n]]], {n, 15}]
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nonn,more
Gus Wiseman, Feb 10 2019
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allocated for Gus Wiseman
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